“The gulf economies are very strange,” says Al-Ubaydli, himself a Bahraini national. He suggests that putting money into Uber, and taking a board seat, gives them a leg up at building a stronger private sector through similar decentralized applications, allowing Saudis -- particularly women, who are less mobile for cultural and legal reasons -- to begin to move the country beyond its dependence on oil revenue.

It's an odd thought, trying to build up the private sector with a targeted investment from the state wealth manager. But given the strange nature of gulf economies, there’s little alternative.

“The normal principles you’re used to deploying in a traditional economy don’t work," Al-Ubaydli says. "I agree it’s a bit ironic, but trying to shift an economy that’s so dependent on oil, you have to think outside of the box.”